Not all bonds are _issued_ as junk. Some may start out investment grade (and thus have a relatively low coupon) and _turn into junk_ meaning that their price would drop due to an increase in the default risk of the issuer.

_Generally_ bonds are issued closed to par, so they would need to pay a higher coupon in order to get a price near par. 

This is one of the reason that yield is such an important measure for bonds. It is a way to compare bonds that have different coupons and prices in a meaningful way.

Note that bonds are classified as "junk" _because_ they have a high risk of default. The price is a reflection of both the coupon amount and the risk of default, so a bond might have a low price OR a high coupon and still not be classified as "junk".